Continuous Set Model Predictive Control Research Articles

A robust microgrid using an inverter with CCS-MPC control and resilient operation

Modern generation trend through renewable energy-based distributed energy resources has made microgrids an important part of the power system. Robust control of the inverter providing quality power has become an essential microgrid (MG) requirement. This paper proposes continuous control set model predictive control (CCS-MPC) on inverter for dynamic voltage regulation supplying reactive power to the load for a MG. The proposed method uses the terminal voltage magnitude, which reduces calculation time, sensor per phase, and the engagement burden of the controller. This paper applies a nonlinear VSI model and a series parallel structure nonlinear autoregressive exogenous (NARX) model of artificial neural network (ANN) to predict future output which CCS-MPC optimizes. The proposed VSI with CCS MPC is applied to a case study of a real system as a plug-and-play device. Simulation shows the satisfactory result of the proposed controller. The inverter control system has been made resilient to protect itself and automatically recover from faults on the DC and AC side, providing quality power to its local load when the fault has been removed.

Smart Control Solution for Single-Stage Solar PV Systems

Solar photovoltaic (PV) systems unpredictable characteristics and tight grid-codes demand power electronic-based energy conversion devices. Hence, as the power levels generated by the solar PV systems rise, multi-level voltage source converters (VSC) and their control mechanisms become more necessary for effective energy conversion. Continuous control set model predictive control (CCS-MPC) is a class of predictive control approach that has emerged recently for the applications of power converters and energy conversion systems. In this paper, an artificial neural network (ANN) based controller for single-stage grid-connected PV is implemented. The CCS-MPC is used as an expert / a teacher to generate the data required for off-line training of the neural network controller. After the off-line training, the trained ANN can fully control the inverter’s output voltage and track the maximum power point (MPP) without the need for MPC during testing. The proposed control technique is assessed under various operating conditions. Based on the results obtained, it is observed that the proposed techniques offer improved objective tracking and comparative dynamic response with respect to the classical approaches.

Model Predictive Control Design and Hardware in the Loop Validation for an Electric Vehicle Powertrain Based on Induction Motors

Electric vehicles (EV) have gained importance in recent years due to environmental pollution and the future scarcity of fossil resources. They have been the subject of study for many years, where much work has focused on batteries and the electric motor (EM). There are several types of motors in the market but the most widely used are induction motors, especially squirrel cage motors. Induction motors have also been extensively studied and, nowadays, there are several control methods used—for example, those based on vector control, such as field-oriented control (FOC) and direct torque control (DTC). Further, at a higher level, such as the speed loop, several types of controllers, such as proportional integral (PI) and model predictive control (MPC), have been tested. This paper shows a comparison between a Continuous Control Set MPC (CCS-MPC) and a conventional PI controller within the FOC method, both in simulation and hardware in the loop (HIL) tests, to control the speed of an induction motor for an EV powered by lithium-ion batteries. The comparison is composed of experiments based on the speed and quality of response and the controllers’ stability. The results are shown graphically and numerically analyzed using performance metrics such as the integral of the absolute error (IAE), where the MPC shows a 50% improvement over the PI in the speed tracking performance. The efficiency of the MPC in battery consumption is also demonstrated, with 5.07 min more driving time.

A Two-Step Continuous-Control-Set MPC for Modular Multilevel Converters Operating With Variable Output Voltage and Frequency

This paper presents a new enhanced single-stage two-step Continuous Control Set Model Predictive Control (CCS-MPC) algorithm, for Modular Multilevel Converters (MMCs) operating with variable output frequency at the AC port. The proposed two-step CCS-MPC allows the implementation of feed-forward compensation of the one-step ahead perturbations at the AC side, using an algorithm based on the Moore-Penrose pseudoinverse matrix. Limitations of the current and voltages in the MMC clusters are implemented to avoid overmodulation and overcurrents, being the solution of the constrained CCS-MPC online solved using the active-set method. Without losing generality, the experimental validation of the single-stage CCS-MPC is performed using an 18-cell MMC prototype, driving a 7.5 kW cage induction machine operating in a wide speed range. A dSPACE MicroLabBox platform is used to control the MMC-based drive by implementing the CCS-MPC algorithm, the modulation stage and the active-set method. It is experimentally demonstrated that the compensation of the low-frequency perturbations allows a considerable reduction in the required circulating currents at the low-frequency operation of the drive. Reduction in the capacitor voltage ripple, improved efficiency, and a smaller Total Harmonic Distortion (THD) in the output currents are also achieved with the proposed single-stage two-step CCS-MPC.

A model predictive control of three‐phase grid‐connected current‐source inverter based on optimization theory

AbstractIn the three‐phase grid‐connected current‐source inverters (CSIs), the resonance result from the AC‐side CL filter and the quality of the grid‐current waveform under the unbalanced and harmonic grid voltage conditions are two issues deserving attention. To solve the two problems, a continuous control set‐model predictive control (CCS‐MPC) method based on the optimization theory is proposed in the two‐phase synchronous coordinate frame in this paper. The constructed cost function takes grid‐connected current and output current of the inverter as control target, and obtains its optimal solution under the least‐squares method, where the optimal inverter‐side current reference is composed of inductor‐current proportional feedback, capacitor‐voltage proportional feedback, and inverter‐side current steady‐state value feedforward. The proposed method can easily realize the normal operation of three‐phase grid‐connected CSIs because the method can be determined by only one parameter under the unbalanced and distorted grids. Furthermore, in the proposed method, the proportional feedback of capacitor voltage can effectively suppress the CL filter resonance. Finally, simulation and experimental results verify the effectiveness of the proposed control strategy.

Dynamic Performance Improvement of Continuous Control Set Model Predictive Control for High-Frequency Link Matrix Converter

In this paper, a comprehensive control strategy of a high frequency link matrix converter (HFLMC) based on the interaction technology between electric vehicle and power grid is proposed to improve the dynamic performance of the system. The continuous control set model predictive control (CCS-MPC) is applied to the current loop to solve the problems of difficult selection of PI control parameters and slow dynamic response speed. In order to ensure that the grid-connected current can achieve better command tracking, a deviation suppression term is introduced into the cost function of CCS-MPC, and the online auto tuning method of weight factors of fast-tracking term and deviation suppression term is designed. On this basis, the PWM signals are generated by the coordinated modulation strategy of the HFLMC to obtain a constant switching frequency, which makes the harmonic of the grid connected current easier to be filtered out. Experimental results show the correctness and feasibility of the proposed control strategy.

Continuous Control Set Model Predictive Control for the optimal current control of Permanent Magnet Synchronous Motors

This paper proposes a Continuous Control Set Model Predictive Control (CCS-MPC) for controlling the internal loop of Permanent Magnet Synchronous Motors (PMSMs). The proposed controller has the ability to track the references with zero steady-state error and provides a fast dynamic response. The performance of the internal loop affects the motor currents and torque ripples. The obtained Total Harmonic Distortion (THD) with the same switching frequency is much lower than Finite Control Set Model Predictive Control (FCS-MPC), which is mostly used in controlling the internal loop.The control parameters are selected with a sensitivity analysis to provide a reasonable phase margin and gain margin. Furthermore, to overcome the nonlinearity of the model, the controller is designed beforehand for different speed setpoints, and the control law coefficients are saved in a look-up table. Then, in each sampling time, the speed is measured, the coefficient is interpolated, and the control law is updated.All the optimization of the proposed controller is performed offline and the output is some simple expressions thus the control law is not computationally expensive. In addition, the controller output is voltage in the continuous space that is applied to the inverter by a standard algorithm and works with a fixed switching frequency.The simulation and experimental results are presented to validate the proposed controller’s appealing features.

Dynamic performance improvement of induction motors used in rolling mill application: A two-loop model predictive control strategy

In this paper, a novel two-loop model predictive control (TLMPC) is proposed to enhance the dynamic performance of induction motors used in rolling mill applications. In such applications, two individual voltage source inverters feed induction motors which are connected to the grid in a back-to-back manner. The grid-side converter, responsible for controlling the DC-link voltage, plays a vital role in the dynamic performance of the induction motors. Its undesired performance deteriorates the speed control of induction motors, which is a crucial need in the rolling mill industry. The proposed TLMPC includes a short-horizon finite set model predictive control in the inner loop to control the power flow by finding the best switching state of the grid-side converter. Additionally, a long-horizon continuous set model predictive control is developed in the outer loop for adjusting the set point value of the inner loop by predicting the DC-link voltage in a limited time horizon. An identification approach is exploited to approximate the non-linear model of the grid-side converter in order to use it in the outer loop. The mathematical proof of the robust stability of the proposed TLMPC is provided and its real-time execution is also certified. Finally, the capability of the proposed approach is evaluated using MATLAB/Simulink. A sensitivity analysis to evaluate the effect of the model’s inaccuracy and uncertainties on the performance of the proposed strategy is also provided.

A Standalone Energy Management System of Battery/Supercapacitor Hybrid Energy Storage System for Electric Vehicles Using Model Predictive Control

In this paper, a standalone model predictive control (MPC)-based energy management strategy (EMS) is proposed for the hybrid energy storage system (HESS) in electric vehicles (EV). The proposed EMS does not require any knowledge of vehicle speed or future demands, so it can be implemented as a standalone system without interfacing with the motor drive system. Furthermore, only one tuning parameter is used to adjust the performance of the proposed MPC-based EMS. The cost function is made of the deviation of the predicted supercapacitor (SC) voltage from its desired value and the difference between the battery current and its steady-state value. Furthermore, the constraints on the battery current rate and the SC voltage will be enforced when solving the optimization problem of EMS. Based on the finite set of battery current references, the online optimal solution can be implemented in the experiment. Then, the fast convergent current control is designed to track the optimal current reference using a continuous control set MPC. To show the effectiveness of the proposed method, the comparison with the rule-based EMS will be presented in simulation and experiments.

Robust Continuous Control Set Model Predictive Control in Synchronous Reference Frame for Grid-Tied Inverters

This article proposes a continuous control set model predictive control (CCS-MPC) for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -based grid-tied inverters. The proposed controller has inherent robustness against <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> resonance and does not need an active damping loop. The controller is designed in the synchronous reference frame where the variables are dc quantified. Otherwise, it can generate a steady-state offset in the stationary frame. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> model, which is needed for the CCS-MPC design, shows a strong cross-coupling between the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> axes, and the order of the model is high. To deal with the cross-coupling, a multi-input multioutput CCS-MPC is designed, and to reduce the order, system identification is used to build the process model. The optimization of CCS-MPC is performed offline, and a low real-time computation is needed. Moreover, the controller’s output is applied by a modulator, and it operates with a fixed switching frequency. To guarantee the closed-loop stability, the controller parameters are selected by a sensitivity analysis. The simulation and experimental results are presented to validate the proposed controller’s appealing features.

Deep Learning-Based Long-Horizon MPC: Robust, High Performing, and Computationally Efficient Control for PMSM Drives

This article presents a computationally efficient and high performing approximate long-horizon model predictive control (MPC) for permanent magnet synchronous motors (PMSMs). Two continuous control set MPC (CCS-MPC) formulations are considered: the classical current tracking delta MPC (Del-MPC) and the torque tracking economic MPC (EMPC). To achieve offset-free torque tracking under model uncertainties and in all regions of operation, a disturbance observer and a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -current reference generator are used. To enable real-time implementation of the long-horizon CCS-MPC, the development of a real-time capable solver is not required, since MPC approximation based on deep neural networks (DNNs) is considered and utilized for controller’s evaluation at run time. The approximation is done by training the DNN to learn the MPC functionality based on offline-generated training data and in an open-loop manner. The robust and offset-free tracking performance of the proposed DNN-based approximate long-horizon Del-MPC and EMPC has been validated through simulation and real-time implementation at test bench and compared to the state-of-the-art field oriented control (FOC) using internal model controller with field-weakening (FW) part and to the exact short-horizon MPC based on the fast gradient method (FGM-MPC). Results show that the long-horizon MPC can achieve significantly faster torque transient responses in comparison with the short-horizon FGM-MPC and the conventional FOC, especially in FW region.

Speed Sensorless Model Predictive Torque Control of Induction Motors Using a Modified Adaptive Full-Order Observer

In this article, a new design of the state observer is proposed to reduce the unstable low-speed region of the adaptive full-order observer (AFO) based speed sensorless speed control of induction motors (IM). The proposed state observer is designed in z-domain rather than in s-domain following the pole-placement approach. The convergence rate of the proposed observer can be made faster than that of the IM poles without extra oscillation effects and the unstable low-speed region of AFO can be reduced to the zero-synchronous-frequency (ZSF) line. Also, a modified adaptation law of the AFO is derived to estimate the rotor speed. Based on the modified AFO, a continuous control set model predictive control (CCS-MPC) is designed for the inner-loop torque control. The cost function of the CCS-MPC is made of the predicted tracking errors on the state and control input. Finally, the dual-loop speed sensorless speed control using the modified AFO and CCS-MPC is presented in simulations and experiments.

Continuous Set Model Predictive Control for Energy Management of Modular Multilevel Matrix Converters

The modular multilevel matrix converter (M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> C) is an ac to ac power converter composed of 9 arms and is proposed for high power applications such as motor drive and wind energy conversion systems. Energy Control of the M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> C is achieved using four circulating currents, and is frequently divided into the different frequency mode (DFM) and equal frequency mode (EFM). EFM is more challenging, because of the larger capacitor voltage oscillations that can be produced. The control schemes are typically different for EFM/DFM operation and this further increases the complexity. In this article, a continuous-control-set model predictive control for energy management of the M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> C is proposed. The control scheme is based on solving an equality constrained quadratic programming problem, where the optimal solution is analytically obtained. The result is a single and simple control law to obtain the circulating current references, where good performance is achieved for both EFM and DFM. The proposed strategy is experimentally validated using a scaled-down M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> C prototype composed of 27 power cells.

Fast Solver for Implicit Continuous Set Model Predictive Control of Electric Drives

This paper proposes a fast and accurate solver for implicit Continuous Set Model Predictive Control for the current control loop of synchronous motor drives with input constraints, allowing for reaching the maximum voltage feasible set. The related control problem requires an iterative solver to find the optimal solution. The real-time certification of the algorithm is of paramount importance to move the technology toward industrial-scale applications. A relevant feature of the proposed solver is that the total number of operations can be computed in the worst-case scenario. Thus, the maximum computational time is known a priori. The solver is deeply illustrated, showing its feasibility for real-time applications in the microseconds range by means of experimental tests. The proposed method outperforms general-purpose algorithms in terms of computation time, while keeping the same accuracy.

A robust passivity based model predictive control for buck converter suppling constant power load

In this paper, the instability problem caused by the constant power load in Buck converter is addressed. In order to solve this instability problem, a composite controller is proposed. Due to the double loop structure of this controller, the passivity based control (PBC) is adopted in the voltage loop to track the reference voltage and make the system stable, while a simplified continuous control set model predictive control (CCS-MPC) is selected as the current controller to track the current reference. Moreover, in order to improve the robustness of the controller and avoid the static error in output, a high order disturbance observer (HODO) is designed out to compensate the negative effects caused by the disturbance and uncertainty. Then, a mixed potential theory based large signal stability analysis is conducted to investigate the large signal stability of the studied system. In order to verify the proposed method, MATLAB simulation, OPAL-RT based hardware in loop and rapid control prototype experiments are conducted.

A novel continuous control set model predictive control to guarantee stability and robustness for buck power converter in DC microgrids

In this paper, an adaptive continuous control set model predictive control (CCS-MPC) is proposed to eliminate the instability problem caused by the constant power load (CPL) in DC–DC​ buck converter applied in DC microgrids. Based on the dynamic model of energy storage elements(inductor and capacitor) in circuit, a parallel feedforward algorithm (PFA) is designed to estimate the variation of the load and input voltage. By supplying the information of the variation to the CCS-MPC controller, the large signal stability and fast recovery performance can be ensured under the existence of disturbances. To verify the control robustness of the adaptive CCS-MPC controller, the MATLAB simulations, hardware-in-loop (HIL) experiments and rapid-control-prototype (RCP) experimental results are conducted. Moreover, the comparative simulations and HIL experiments towards other nonlinear controller are conducted to investigates its dynamic performance.

A Comparison of Finite Control Set and Continuous Control Set Model Predictive Control Schemes for Model Parameter Mismatch in Three-Phase APF

Model predictive control (MPC) methods are widely used in the power electronic control field, including finite control set model predictive control (FCS-MPC) and continuous control set model predictive control (CCS-MPC). The degree of parameter uncertainty influence on the two methods is the key to evaluate the feasibility of the two methods in power electronic application. This paper proposes a research method to analyze FCS-MPC and CCS-MPC’s influence on the current prediction error of three-phase active power filter (APF) under parameter uncertainty. It compares the performance of the two model predictive control methods under parameters uncertainty. In each sampling period of the prediction algorithm, different prediction error conditions will be produced when FCS-MPC cycles the candidate vectors. Different pulse width modulation (PWM) results will be produced when CCS-MPC solves the quadratic programming (QP) problem. This paper presents the simulation results and discusses the influence of inaccurate modeling of load resistance and inductance parameters on the control performance of the two MPC algorithms, the influence of reference value and state value on prediction error is also compared. The prediction error caused by resistance mismatch is lower than that caused by inductance mismatch, more errors are caused by underestimating inductance values than by overestimating inductance values. The CCS-MPC has a better control effect and dynamic performance in parameter mismatch, and the influence of parameter mismatch is relatively tiny.

Stabilization of Constant Power Loads in DC Microgrid Systems Using an Adaptive Continuous Control Set Model Predictive Control

This paper represents an adaptive continuous control set model predictive control (CCS-MPC) to solve the disturbance-caused instability problems in a DC microgrid consisting of symmetrical parallel buck converters, constant voltage loads (CVL), and constant power loads (CPL). The symmetric model of the system is founded at first to describe and analyze the disturbance-caused instability problem. To mitigate the instability by taking the disturbances into consideration, the proposed adaptive controller is made from a double loop feedback controller and a feedforward estimation algorithm. In the voltage loop of the double loop controller, a capacitor dynamic-based voltage controller is developed, while in the current loop, a CCS-MPC algorithm is modified and applied. Meanwhile, a feedforward algorithm is developed to estimate the disturbance information and send it to the double loop controller to improve its robustness, so the composite controller can maintain the bus voltage fixed at its reference and the symmetrical equal current sharing. Finally, comparative MATLAB simulations and OPAL-RT hardware-in-the-loop experiments are conducted to verify the effectiveness and dynamic performance of the proposed algorithm towards other previous nonlinear controllers.

Hybrid Model Predictive Control of DC–DC Boost Converters With Constant Power Load

This article presents a hybrid model predictive controller to ensure dc microgrid stability and enhance the performance of dc-dc boost converters interfaced with constant power loads (CPLs) in a hybrid system. Hybrid systems are dynamic systems with both continuous current mode and discontinuous current mode states. The main purpose in this article is to develop an advanced control technique for voltage regulation and stabilization of the converters in the presence of CPLs due to serious stability concerns, without considering the accurate modelling information of the system. In this regard, an automatic model, considering different modes of operation induced by semiconductor switches in dc-dc boost converters and highly non-linear nature of CPL is employed to design the proposed control approach. The non-linear CPL connected directly to a dc-dc boost converter is utilized to define an optimal tracking control problem by minimizing a finite-prediction horizon cost function, which is known as a finite control set MPC. The proposed controller, which is implemented in both continuous and discontinuous current modes, accounts for the regulation of output voltage within the predefined range. The effectiveness of the proposed hybrid model predictive control is verified using a comparative evaluation with discrete-time averaged model predictive control, continuous control set MPC, and the conventional PI control under experimental conditions. The results authenticate an improved dynamic performance, which can be applied to practical dc microgrids with CPLs.

Improved Continuous Control Set Model Predictive Control for Three-Phase CVCF Inverters: Fuzzy Logic Approach

This paper presents an improved continuous control set model predictive control (CCS-MPC) scheme using a fuzzy logic approach (FLA) for three-phase constant voltage constant frequency (CVCF) inverters with an output LC filter. The proposed method can enhance the output voltage quality by using an optimal predictive control law (OPCL). Additionally, the proposed method corrects the input voltage commands through the FLA-based online gain tuning aiming to satisfy the hardware constraint. Thus, the proposed FLA-based CCS-MPC can guarantee an acceptable output voltage with a faster transient response, smaller steady-state error (SSE), and lower total harmonic distortion (THD). Moreover, a Kalman filter-based load current observer is used to significantly improve the reliability and robustness. Comparative experimental studies with another CCS-MPC method are conducted on a prototype three-phase CVCF inverter using TI TMS320F28335 DSP to validate the improved performance under the step-changes of linear/unbalanced/nonlinear loads with uncertain parameters.